Googol-ex-terrible tethrathoth is equal to E100#^^#>#(1+E100) using Extended Cascading-E Notation.[1] The term was coined by Sbiis Saibian.

Approximations in other notations

Notation Approximation
BEAF \(\{100,\text{googol}+1 (X \uparrow\uparrow (X^2)) 2\}\)[2]
Bird's array notation \(\{100,\text{googol}+1 [1 \backslash 1,2] 2\}\)
X-Sequence Hyper-Exponential Notation \(100\{X>X\}\text{googol}+1\)
Fast-growing hierarchy \(f_{\varepsilon_{\omega}}(\text{googol})\)
\(\approx f_{\varepsilon_\omega}(f_2(324))\)
Hardy hierarchy \(H_{\varepsilon_{\omega}}(\text{googol})\)
Slow-growing hierarchy \(g_{\vartheta(\varepsilon_{\Omega \omega})}(\text{googol}+1)\)


  1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2017-01-02.
  2. Using particular notation \(\{a,b (A) 2\} = A\ \&\ a\) with prime b.
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